Perturbed asymptotically linear problems

Preprint English OPEN
Bartolo, R.; Candela, A. M.; Salvatore, A.;
(2012)
  • Subject: 35J20, 58E05 | Mathematics - Analysis of PDEs

The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in t... View more
  • References (17)
    17 references, page 1 of 2

    [1] H. Amann, E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa 7 (1980), 539-603.

    [2] A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.

    [3] P. Bartolo, V. Benci, D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity, Nonlinear Anal. 7 (1983), 981-1012.

    [4] V. Benci, On the critical point theory for indefinite functionals in the presence of symmetries, Trans. Am. Math. Soc. 274 (1982), 533-572.

    [5] V. Benci, A. Capozzi, D. Fortunato, Periodic solutions of Hamiltonian systems with superquadratic potential, Ann. Mat. Pura Appl. CXLIII (1986), 1-46.

    [6] J. Cossio, S. Herr´on, C. V´elez, Existence of solutions for an asymptotically linear Dirichlet problem via Lazer-Solimini results, Nonlinear Anal. 71 (2009), 66-71.

    [7] M. Degiovanni, S. Lancelotti, Perturbations of even nonsmooth functionals, Differential Integral Equations 8 (1995), 981-992.

    [8] M. Degiovanni, S. Lancelotti, Perturbations of critical values in nonsmooth critical point theory, in “Well-posed Problems and Stability in Optimization” (Y. Sonntag Ed.), Serdica Math. J. 22 (1996), 427-450.

    [9] M. Degiovanni, V. Raˇdulescu, Perturbations of nonsmooth symmetric nonlinear eigenvalue problems, C.R. Acad. Sci. Paris S´er. I 329 (1999), 281-286.

    [10] M.A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Translated from the Russian edition, Moscow, 1956 (A.H. Armstrong, J. Burlak Eds), Pergamon, London; Macmillan, New York, 1964.

  • Metrics
Share - Bookmark